Question

Solve x + 3y + z = 1

2x – y – z = 6
5x + y + z = 1 
using matrices.

 

Can you help me figure out this matrix?

Answer 1

Given the eqns

x + 3y +z = 1

2x - y -z =6

5x + y + z =1

let ....A=

1   3   1          1

2   -1  -6  =     6

5    1   1          1

Det(A) =1(0) - 3(7) +1(7)

=-14

• By substituting the values of x by the column 1  6  1

det(A1) = 1(0) -3(7)+1(7)

=-14

X=Det(A1)/Det(A)

= -14/-14

X = 1

By substituting the values of y by the column 1  6  1

det(A2)=1(7) -1(7) +1(-28)

=-28

Y=Det(A2)/Det(A)

=-28/-14

=2

• By substituting the values of z by the column 1  6  1

Det(A3)=1(-7) -3(-28) +1(7)

=84

Z=det(A3)/det(A)

=84/-14

=-6

Therefore the values (x,y,z)=(1,2,-6)